Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras

Abstract

We argue that the Landau-Hall states provide a suitable framework for formulating the Berezin-Toeplitz quantization of classical functions on a Kähler phase space. We derive the star-products for such functions in this framework and generalize the Berezin-Toeplitz quantization to matrix-valued classical functions. We also comment on how this is related to different calculations of the effective action for Hall systems.

16 pages

References in corpus (6)

• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Toeplitz operators on symplectic manifolds
• Entanglement entropy and Berezin-Toeplitz operators
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory

Cited by in corpus (5)

• Matrix Quantization of Gravitational Edge Modes
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• The matrix regularization for Riemann surfaces with magnetic fluxes
• Laplacians on Fuzzy Riemann Surfaces
• Deformation of Matrix Geometry via Landau Level Evolution